Problem: There are 9 people in a room. If everyone shakes everyone else's hand exactly once, how many handshakes occur?
Given 9 people, each person shakes the hands of 8 other people. The following is almost the answer. $9 \times 8 = 72$ We have double counted the handshakes though, since Daniel shaking Emily's hand is the same handshake as Emily shaking Daniel's hand. Therefore, the following is the correct answer. $\dfrac{9 \times 8}{2} = 36$